Entropy in Dynamical Systems.

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A comprehensive course on entropy in dynamical systems ideal for graduate students learning the subject from scratch.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Downarowicz, Tomasz
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2011.
Colección:New mathematical monographs.
Temas:
Topological entropy > Textbooks.
Topological dynamics > Textbooks.
Mathematics.
MATHEMATICS > General.
Topological dynamics
Topological entropy
Textbooks
Acceso en línea:Texto completo

MARC

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100 1 |a Downarowicz, Tomasz. 
245 1 0 |a Entropy in Dynamical Systems. 
260 |a Cambridge :  |b Cambridge University Press,  |c 2011. 
300 |a 1 online resource (406 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a New Mathematical Monographs ;  |v v. 18 
505 0 |a Cover; Entropy in Dynamical Systems; NEW MATHEMATICAL MONOGRAPHS; Title; Copyright; To my Parents; Contents; Preface; Acknowledgments; Introduction; 0.1 The leitmotiv; 0.2 A few words about the history of entropy; 0.3 Multiple meanings of entropy; 0.3.1 Entropy in physics; 0.3.2 Shannon entropy; 0.3.3 Connection between Shannon and Boltzmann entropy; 0.3.4 Dynamical entropy; 0.3.5 Dynamical entropy as data compression rate; 0.3.6 Entropy as disorder; 0.4 Conventions; Part I Entropy in ergodic theory; 1 Shannon information and entropy; 1.1 Information and entropy of probability vectors. 
505 8 |a 1.2 Partitions and sigma-algebras1.3 Information and static entropy of a partition; 1.4 Conditional static entropy; 1.5 Conditional entropy via probabilistic tools*; 1.6 Basic properties of static entropy; 1.7 Metrics on the space of partitions; 1.8 Mutual information*; 1.9 Non-Shannon inequalities*; Exercises; 2 Dynamical entropy of a process; 2.1 Subadditivity; 2.2 Preliminaries on dynamical systems; 2.3 Dynamical entropy of a process; 2.4 Properties of dynamical entropy; 2.5 Affinity of dynamical entropy; 2.6 Conditional dynamical entropy via disintegration* 
505 8 |a 2.7 Summary of the properties of entropy2.8 Combinatorial entropy; Exercises; 3 Entropy theorems in processes; 3.1 Independence and e-independence; 3.2 The Pinsker sigma-algebra in a process; 3.3 The Shannon-McMillan-Breiman Theorem; 3.4 The Ornstein-Weiss Return Times Theorem; 3.5 Horizontal data compression; Exercises; 4 Kolmogorov-Sinai Entropy; 4.1 Entropy of a dynamical system; 4.2 Generators; 4.3 The natural extension; 4.4 Joinings; 4.5 Ornstein Theory*; Exercises; 5 The Ergodic Law of Series*; 5.1 History of the Law of Series; 5.2 Attracting and repelling in signal processes. 
505 8 |a 5.3 Decay of repelling in positive entropy5.3.1 The idea of the proof and the basic lemma; 5.3.2 The proof of Theorem 5.3.3; 5.4 Typicality of attracting for long cylinders; Part II Entropy in topological dynamics; 6 Topological entropy; 6.1 Three definitions of topological entropy; 6.1.1 The metric definition via separated orbits; 6.1.2 The metric definition via spanning orbits; 6.1.3 The topological definition via covers; 6.1.4 Relations between the above notions; 6.2 Properties of topological entropy; 6.3 Topological conditional and tail entropies. 
505 8 |a 6.4 Properties of topological conditional entropy6.5 Topological joinings; 6.6 The simplex of invariant measures; 6.7 Topological fiber entropy; 6.8 The major Variational Principles; 6.9 Determinism in topological systems; 6.9.1 Topological analogs of determinism; 6.9.2 Hierarchy of maximal factors; 6.10 Topological preimage entropy*; Exercises; 7 Dynamics in dimension zero; 7.1 Zero-dimensional dynamical systems; 7.2 Topological entropy in dimension zero; 7.3 The invariant measures in dimension zero; 7.4 The Variational Principle in dimension zero. 
500 |a 7.5 Tail entropy and asymptotic h-expansiveness in dimension zero. 
520 |a A comprehensive course on entropy in dynamical systems ideal for graduate students learning the subject from scratch. 
588 0 |a Print version record. 
504 |a Includes bibliographical references (pages 379-385) and index. 
546 |a English. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Topological entropy  |v Textbooks. 
650 0 |a Topological dynamics  |v Textbooks. 
650 4 |a Mathematics. 
650 7 |a MATHEMATICS  |x General.  |2 bisacsh 
650 7 |a Topological dynamics  |2 fast 
650 7 |a Topological entropy  |2 fast 
655 7 |a Textbooks  |2 fast 
758 |i has work:  |a Entropy in Dynamical Systems (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCFwPGBrwcCP4RYTpVhYXVC  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Downarowicz, Tomasz.  |t Entropy in Dynamical Systems.  |d Cambridge : Cambridge University Press, ©2011  |z 9780521888851 
830 0 |a New mathematical monographs. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=807302  |z Texto completo 
880 0 |6 505-00/(S  |a Cover -- Entropy in Dynamical Systems -- NEW MATHEMATICAL MONOGRAPHS -- Title -- Copyright -- To my Parents -- Contents -- Preface -- Acknowledgments -- Introduction -- 0.1 The leitmotiv -- 0.2 A few words about the history of entropy -- 0.3 Multiple meanings of entropy -- 0.3.1 Entropy in physics -- 0.3.2 Shannon entropy -- 0.3.3 Connection between Shannon and Boltzmann entropy -- 0.3.4 Dynamical entropy -- 0.3.5 Dynamical entropy as data compression rate -- 0.3.6 Entropy as disorder -- 0.4 Conventions -- Part I Entropy in ergodic theory -- 1 Shannon information and entropy -- 1.1 Information and entropy of probability vectors -- 1.2 Partitions and sigma-algebras -- 1.3 Information and static entropy of a partition -- 1.4 Conditional static entropy -- 1.5 Conditional entropy via probabilistic tools* -- 1.6 Basic properties of static entropy -- 1.7 Metrics on the space of partitions -- 1.8 Mutual information* -- 1.9 Non-Shannon inequalities* -- Exercises -- 2 Dynamical entropy of a process -- 2.1 Subadditivity -- 2.2 Preliminaries on dynamical systems -- 2.3 Dynamical entropy of a process -- 2.4 Properties of dynamical entropy -- 2.5 Affinity of dynamical entropy -- 2.6 Conditional dynamical entropy via disintegration* -- 2.7 Summary of the properties of entropy -- 2.8 Combinatorial entropy -- Exercises -- 3 Entropy theorems in processes -- 3.1 Independence and ε-independence -- 3.2 The Pinsker sigma-algebra in a process -- 3.3 The Shannon-McMillan-Breiman Theorem -- 3.4 The Ornstein-Weiss Return Times Theorem -- 3.5 Horizontal data compression -- Exercises -- 4 Kolmogorov-Sinai Entropy -- 4.1 Entropy of a dynamical system -- 4.2 Generators -- 4.3 The natural extension -- 4.4 Joinings -- 4.5 Ornstein Theory* -- Exercises -- 5 The Ergodic Law of Series* -- 5.1 History of the Law of Series -- 5.2 Attracting and repelling in signal processes. 
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